According to [1]}, the solution \(u(t,x)\)  of the system (REF ) can be rewritten as
\(u(t) =\sum _{k=1}^{\infty }\left\lbrace \langle u_0,\phi _k\rangle E_{\alpha ,1}(-\lambda _k t^\alpha )+\int _0^t(t-\tau )^{\alpha -1}E_{\alpha ,\alpha }(-\lambda _k (t-\tau )^\alpha )\langle f(u(\tau )),\phi _k\rangle \,{\mathrm {d}}\tau \right\rbrace \phi _k.\) 
